Great question! I often see ring systems with a tilted ring in
science fiction movies and cartoons, and it always makes me
wince.
In general, planetary rings are found in the equator plane of
the planet. However, you're right, an inclined ring could form
from the breakup of an object that was on an inclined orbit.
The ring would start with all of the ring particles following
very similar orbits, much like the original body's orbit. Over a
long time (thousands of years, roughly) the ring would spread out
because of the effect of the planet's gravity on the orbit of
each ring particle. All planets bulge a bit at the equator, and
this equatorial bulge tends to turn, or precess, inclined orbits.
Depending on exactly how dense the ring was, and how big the
particles were, it could either evolve into into a ribbon-like
structure or a torus. For the ribbon-like structure, imagine a
belt looped around the planet. It would be thin in radial
extent, but its height would be the height of the object's
inclined orbit above and below the equatorial plane. A torus (as
you probably know) is like a doughnut; it would be the more
scrambled ring that would result if there were a lot of
collisions between ring particles.
Over time, as the ring particles continued to collide, the ring
would collapse down into the equatorial plane.
Now, that having been said, there are inclined rings around
Saturn, Uranus and Neptune! These rings are "shepherded" by
satellites, and since the satellites are in inclined orbits, they
keep their "sheep" in an inclined ring. However, these rings
aren't like the beautiful broad main rings of Saturn; they are
kept very narrow and tightly confined by their shepherd moons.
Also, their inclinations are very small. For example, I work on
the F ring of Saturn, with its shepherd moons, Prometheus and
Pandora, has an inclinaton of only 0.0016 degrees. This may seem
almost too tiny to matter, but it turns out to be very important
when the rings of Saturn are viewed edge-on, and the effects on
the brightness of the rings are what I'm currently writing about
for my thesis.
As another example, Cordelia and Ophelia
shepherd Uranus' Epsilon ring at an angle of about 0.1 degrees.